Data processing apparatus for chromatograph

ABSTRACT

A method of properly correcting a base line. A concept of flexibility of a base line is introduced as an input index and a gravitation is presumed between the base line and signal data which is measured, thereby constructing a method of correcting the base line which changes gentler than a change in signal with respect to time in a peak area and which is sensitive to an area where a value of the signal data is small. A base line like a natural and smooth curve which isn&#39;t easily influenced by a local change in signal such as noise or the like can be set by an input of the flexibility.

[0001] This is a continuation of application Ser. No. 09/562,026 filedMay 1, 2000, which is a continuation of Ser. No. 08/605,416 filed Feb.22, 1996, now U.S. Pat. No. 6,076,047.

BACKGROUND OF THE INVENTION

[0002] 1. [Industrial Field of Application]

[0003] The present invention relates to a data processing apparatus fora chromatograph and, more particularly, to a method of correcting a baseline.

[0004] 2. [Prior Art]

[0005] According to Japanese Patent No. 1,385,425 (Japanese PatentPublication No. 61-54181), as a method of correcting a base line ofnon-separation peaks, there are: (1) the N method, (2) the θ method, and(3) the method of merely connecting a base portion by a straight line(non-correction method).

[0006] In the N method, the number of peaks (N) is designated, N peaksare collected as one peak, and either a base portion or a trough portionis connected by a straight line (FIG. 3(A)). The base portion is aportion that is judged as not a peak area by using a change amount ofsignal as an index.

[0007] In the θ method, an inclination is intentionally loosened whenthe inclination seems to be too steep in the N method (FIG. 3(B)).

[0008] The non-correction method is a most typical method and iseffective when the base line is estimated to be like a straight line(FIG. 3C). In addition, there is also a case of correcting a base lineby intentionally selecting a forward horizon method (FIG. 3D), abackward horizon method (FIG. 3E), a special processing method of ashoulder peak (FIG. 3F), or the like in accordance with a peak shape ofeach chromatogram.

[0009] [Problems that the Invention is to Solve]

[0010] Each of the above base line correcting methods has both meritsand demerits and is selected depending on a particular case, since it isdifficult to unconditionally determine the base line. Although somemethods in which the base line is unconditionally determined have beenproposed (Japanese Patent Application Laid-Open Sho 62-32360, JapanesePatent Application Laid-Open Sho 63-88443, Japanese Patent ApplicationLaid-Open Hei 6-94696, and the like), those methods are not yetgenerally used.

[0011] In all of the above methods, the base line is corrected on thebasis of the base or trough portion existing in the chromatogram.

[0012] An algorithm of searching the base or trough portion generallytends to be too sensitive to a local fluctuation in a signal. Forexample, a case where the trough portion is detected and a case where itis not detected occur depending on a magnitude of noise. A detection ofa starting point and an ending point of a peak, that is, an end pointdetection of the base portion is also disturbed by noise. After all,such a correction of the base line is easily affected by noise and quitedifferent base lines may be obtained due to a slight difference insignals.

[0013] By a similar reason; there is a case where the base line largelyfluctuates when parameters such as sensitivity, slope, and the like, todetect the base portion or trough portion, are improper.

[0014] In the case where the base line is experientially estimated to behorizontal, if a horizontal straight line is applied to the baseportion, a proper base line can be obtained. In the case where the baseline may possibly not be horizontal, however, a method of obtaining thebase line by continuing the base or trough portion with a straight linelike a graph of polygonal line is not always proper.

SUMMARY OF THE PRESENT INVENTION

[0015] It is an object of the invention to provide a data processingapparatus for a chromatograph, which solves the above problems, forms astable base line without being affected by a local noise of achromatogram, and corrects the base line irrespective of localfluctuations of a chromatograph.

[0016] In a data processing apparatus for a chromatograph comprisingbase line determining means for detecting an output value of a detectorfor a chromatograph obtained with the elapse of time, forming achromatogram on the basis of the detection result, and determining abase line on the basis of a shape of the chromatogram, when the baseline is corrected, a deviation in the direction of the output valuebetween each of forming points which form the base line and a formingpoint adjacent to the forming point is largely reduced as the deviationbecomes larger.

[0017] Adjusting means of the base line adjusts so as to reduce a changeamount of the deviation proportional to the deviation with an increasein the deviation and to increase the change amount of the deviationproportional to the deviation with a decrease in the deviation.

[0018] Further, an adjusting range of the adjusting means from a baseline is determined on the basis of the shape of the chromatogram to alinear base line connecting base lines before and after a time zone inwhich the chromatogram appears as a measuring target appears.

[0019] There is also provided selecting means for applying the aboveconstruction to an optional time zone of the measurer.

[0020] In the time zone in which the chromatogram appears as a measuringtarget sample, the deciding means for deciding the base line on thebasis of the shape of the chromatogram decides the base line on thebasis of a distance on the same time base from either one of a straightline connecting a starting point and an ending point of the time zone inwhich the chromatogram appears, a straight line connecting the startingpoint and the trough portion of the chromatogram, and a straight lineconnecting the ending point and the trough portion of the chromatogramto the chromatogram, and arranges a forming point of the base line so asto shorten a distance on the same time base from the straight line forthe distance to the base line with an increase in the foregoingdistance.

[0021] In one mode of the arrangement of forming points on the baseline, the base line is set to the same line as the chromatogram in thetime zone in which the foregoing distance is equal to a value whichranges from zero to a predetermined value.

[0022] The base line of the chromatogram inherently has a very loosechange as compared with the signal change in the peak area and itschange width is narrow.

[0023] That is, when the base line is regarded as a collection of aplurality of points, it is considered that two neighboring points amongthe points are loosely bound to each other. Namely, a base line of ashape having a local projection is impossible. If the base line having alocal projection is drawn, it is considered that the portion isprojected due to improper drawing means of the base line or an influenceby noise occurring somewhere in a chromatograph device.

[0024] In consideration of the above, when the base line drawn byvarious means is regarded as one line constructed by a plurality ofpoints, the correction is performed so as to reduce a deviation in thedirection of the output value between the two adjacent points among thepoints as the deviation becomes large, so that the base line adapted tothe above condition can be drawn.

[0025] The base line drawn as mentioned above can be adjusted whilemaintaining a gentle line in a manner such that when the deviationbetween the two points in a time zone is increased, a change amount ofthe deviation is reduced in proportion to the increase in the deviationand, when the deviation is reduced, the change amount of the deviationis increased in proportion to the decrease in the deviation.

[0026] Another characteristic of the base line is such that the baseline is strongly attracted to an area in which a signal value expressedby the chromatogram is small.

[0027] It is because the signal value that is caused by anothercomponent which is a factor of the noise is unlikely to appear in thetime zone in which a target component appears and an output value whichis not so large is generated since it corresponds to an amount of noiseafter all, and the like.

[0028] In consideration of the above, the base line corresponding to theabove characteristic can be drawn by arranging the forming points of thebase line in a manner such that as the distance in the time basedirection from the chromatogram to the base line as a reference (linearbase line connecting base lines before and after the time zone in whichthe chromatogram as a measuring target appears) becomes longer, adistance in the same time zone from the straight line for the foregoingdistance to the base line is largely reduced.

[0029] When the drawing means of the base line and the correcting meansof the base line are used together, since the projected portion of thebase line drawn by the drawing means can be corrected by the correctingmeans of the base line, the correction of the base line in which the twocharacteristics of the base line are considered can be performed.

BRIEF DESCRIPTION OF THE DRAWINGS

[0030]FIG. 1 is a diagram showing an example of a physical model of theinvention;

[0031] FIGS. 2A-2B are diagrams showing problems of a conventionalmethod;

[0032] FIGS. 3A-3F are diagrams showing a conventional method ofcorrecting a base line;

[0033]FIG. 4 is a diagram showing a construction of a data processingapparatus according to an embodiment of the invention;

[0034] FIGS. 5A-5B are diagrams showing output examples of achromatogram;

[0035]FIG. 6 shows an input screen of gravitation types;

[0036]FIG. 7 shows a profile of a gravitation of a step function type;

[0037]FIG. 8 is an explanatory diagram of advantages of the embodimentof the invention;

[0038] FIGS. 9A-9B are diagrams showing an example of a time program offlexibility;

[0039]FIG. 10 is a diagram showing an example of a connection of baseportions;

[0040]FIG. 11 is a diagram showing an example of a separation of ashoulder peak;

[0041]FIG. 12 is an explanatory diagram of a base line envelope method;

[0042]FIG. 13 is a diagram showing an overlay of a base line;

[0043]FIG. 14 is a diagram of an output example showing reproducibilityof a quantitative value;

[0044]FIG. 15 is a flowchart showing a condition setting for a base linecorrection before a signal is taken in;

[0045]FIG. 16 is a flowchart showing a condition setting for the baseline correction after a signal is taken in;

[0046]FIG. 17 is a flowchart 1 showing a condition setting for the baseline correction;

[0047]FIG. 18 is a flowchart 2 showing a condition setting for the baseline correction;

[0048]FIG. 19 is a flowchart 3 showing a condition setting for the baseline correction;

[0049]FIG. 20 is a flowchart 4 showing a condition setting for the baseline correction;

[0050]FIG. 21 is a flowchart 5 showing a condition setting for the baseline correction;

[0051]FIG. 22 is a flowchart 6 showing a condition setting for the baseline correction;

[0052]FIG. 23 is a flowchart 1 showing an over display of a base line;

[0053]FIG. 24 is a flowchart 2 showing an over display of a base line;

[0054]FIG. 25 is a diagram showing an overlay of the chromatogram;

[0055]FIG. 26 is a diagram showing a manual pick up method;

[0056]FIG. 27 is a flowchart 1 showing the manual pick up method;

[0057]FIG. 28 is a flowchart 2 showing the manual pick up method; and

[0058] FIGS. 29A-29D are explanatory diagrams of a second base lineenvelope method.

DETAILED DESCRIPTION

[0059] An embodiment of the invention will be described hereinbelow withreference to FIG. 4. FIG. 4 is a block diagram of a data processingapparatus for a chromatograph to which the invention is applied. In FIG.4, reference numeral 1 denotes a central processing unit (CPU); 2 aperipheral equipment connecting unit; 3 an A/D converter; 4 a signaldata memory; 5 a control command memory; 6 an input device; 7 an outputdevice; 8 a result data memory; 9 a process parameter memory; and 10 adetector for a chromatograph.

[0060] An analog signal from the detector 10 for a chromatograph isconverted to a digital signal by the A/D converter 3 and is supplied tothe CPU 1 through the peripheral equipment connecting unit 2. By acommand in the control command memory 5, the signal is converted tosignal data of a predetermined format and the data is stored into thesignal data memory 4.

[0061] An embodiment of forming means of a base line of a chromatogramand correcting means of the base line of the formed chromatogram of theinvention will now be described.

[0062] According to the embodiment, the base line is formed andcorrected on the basis of two characteristics of the base line of thechromatogram. The two characteristics are such that the base line isstrongly attracted to an area in which a signal value expressed by thechromatogram is small and that neighboring points in the base lineformed by continuous points are loosely bound.

[0063] The former characteristic is coped with in a manner such that asa distance between each of continuous points which form the chromatogramand a forming point of a reference base line (in the embodiment, a lineobtained by connecting base lines before and after a time zone in whicha peak of a measuring target sample appears) in the same time basedirection becomes large, a ratio of length between the straight line forthe distance and the forming point of the base line is reduced.

[0064] That is, as the reference base line on the same time base becomescloser to the chromatogram, the reference base line is stronglyattracted to the chromatogram. It can be defined that gravitation ormagnetism acts between the chromatogram and the reference base line onthe same time base from this point of view, since when the distance islong, only a weak force acts, and when the distance is short, a strongforce acts.

[0065] The latter characteristic is coped with in a manner such that thelonger a distance in the time base direction between the adjacent pointsamong the continuous points which form the base line is, the more thedistance is reduced.

[0066] When a physical idea is adapted to the above, the characteristicof spring can be considered since the more a spring is stretched, thestronger a force acts.

[0067] A formation of the base line in consideration of the twocharacteristics of the base line will now be considered.

[0068]FIG. 1 is a diagram showing a specific physical image consideringthe two characteristics. Although a two-dimensional elastic body(spline) or plastic body (adjustable ruler) or the like can beintroduced as a base line, the formation of the base line is consideredhere in a category of dynamics of a one-dimensional elastic body,particularly, statics in which a balance of forces used for simplicityof explanation.

[0069] A signal waveform doesn't move and points each having pluscharges are fixed at equal intervals. Particles having minus charges arearranged on the base line so as to correspond to the plus charges. It isnow assumed that a Coulomb force acts only between the plus and minuscharges on the same x-coordinate. The particles of minus charges cannotfreely move and the neighboring particles are connected by a spring. Amodel wherein two or three neighboring particles are weighted andconnected by a spring is also possible. It is also assumed thatelasticity of the spring works only in the vertical direction (Ydirection). That is, axes attached to blank circles in FIG. 1 move onlyin the vertical direction and don't rotate.

[0070] The straight base line is horizontally lifted from the lower partof signal data. The straight line is rotated by using a point which iscontacted for the first time as an axis and a point to be contacted nextis obtained. The straight line is rotated right and left and a contactpoint which is located further from the axis is used. A gravitation isacted in this instance and the base line is allowed to be curved. Thesignal data and the base line make contact at a point where thegravitation acts more than the elasticity of spring which acts againstto be curved.

[0071] Expression 1 shown below is a balance equation of force on anoptional x-coordinate.

[0072] balance equation of force: $\begin{matrix}{{{K\frac{q^{2}}{\left( {Y_{i} - y_{i}} \right)^{2}}} - {k\left( {y_{i} - y_{i - 1}} \right)} - {k\left( {y_{i} - y_{i + 1}} \right)}} = 0} & \left\lbrack {{expression}\quad 1} \right\rbrack\end{matrix}$

[0073] where,

[0074] K: constant of Coulomb force

[0075] Y₁: (i)th signal data point (constant)

[0076] q: charge (constant)

[0077] y_(i): (i)th base line point (variable)

[0078] k: spring constant

[0079] The condition is Y_(i)≧y_(i). When Y_(i)=y_(i), the balanceequation is unnecessary.

[0080] y_(i−1), y_(i), y_(i+1), and the like are variables and theothers are constants. A point where an actual signal value Y_(j) and abase line y_(j) are equal, namely, a point of contact is eliminated fromthe balance equation and the number of equations is set to n. Although nvariables can be obtained from the n balance equations, it is moreefficient to solve the equation by approximating it to a linear equationsuch as Y_(i) or the like as shown below.

[0081] When Y_(i)>>y_(i): $\begin{matrix}{{{\frac{K_{q}^{2}}{Y_{i}^{2}}\left( {1 + \frac{2y_{i}}{Y_{i}}} \right)} - {k\left( {y_{i} - y_{i - 1}} \right)} - {k\left( {y_{i} - y_{i + 1}} \right)}} = 0} & \left\lbrack {{expression}\quad 2} \right\rbrack\end{matrix}$

[0082] The base line obtained as mentioned above is shown by blank dotsin FIG. 1. Although the number of dots expressed is small in FIG. 1, acalculation is actually performed by using all of the sampling points.By correcting the base line with such a model, the base line isn'texcessively curved and the base line which is properly contacted andclose to a portion where the signal value is small can be obtained. Thatis, flexibility of the base line is characterized by parameters ofstrength of materials such as spring constants and the like, therebypreventing a rapid local change. The signal data and the base line areattracted by a gravitation force having a distance dependency such asthe Coulomb force or the like, so that the base line can be broughtespecially strongly close to an area where the value of the signal datais small.

[0083] In case of actually properly correcting the base line by dataprocessing apparatus, an index such as strength of flexibility is inputas a parameter like the spring constant and a distance dependency ofgravitation (inverse-square type, exponential function type, stepfunction type, and the like) is designated.

[0084] Although the base line has been formed and corrected on the basisof the two characteristics of base line in the illustrated embodiment,the base line can also be formed and corrected by taking account of onlyone of the two characteristics.

[0085] That is, it is also possible to form the base line by base lineforming means as in the conventional technique, input the index ofstrength of the flexibility, such as spring constant, as a parameter,according to the invention, smooth a projected portion in the base lineobtained by using the base line forming means which depends on thedistance between the chromatogram and the reference base line of theinvention, and the like.

[0086] Various concepts can be included in the base line correctionaccording to the embodiment of the invention as mentioned above.Selecting means will now be described in accordance with the order ofsteps of the base line correction.

[0087] Parameters for the base line correction have preliminarily beenstored into the process parameter memory 9 from the input device 6before a signal is taken in (FIG. 15). The following inputting operationwill be also similarly executed in a case of again performing the baseline correction to the signal data once taken in (FIG. 16).

[0088] The type of gravitation is selected from another picture screen(FIGS. 6 and 17). Although a parameter of a gravitation constant has tobe inherently set, the input can be omitted since it is in relativerelation to the flexibility of the base line. Parameters regarding adistance (pV) between the signal data and the base line have to beinput. A characteristic distance ro is directly input by a numericalvalue (μV) or can also be automatically set by a peak height, a valuethat is constant times as large as noise, or the like.

[0089] The inverse-square type gravitation relates to an interactiongenerally existing in the natural world such as Coulomb force,gravitation, or the like and has the shape of expression 3, as shownbelow. The exponential function type gravitation is expressed byexpression 4 as shown below and when the distance becomes long, thegravitation rapidly attenuates as compared with that of theinverse-square type. $\begin{matrix}{{f(r)} = \frac{1}{r^{2}}} & \left\lbrack {{expression}\quad 3} \right\rbrack \\{{f(r)} = {\left. e^{{- r}/r_{0}} \right.\sim\left\{ \frac{1 - {\frac{r}{r_{0}}\left( {r{\operatorname{<<}r_{0}}} \right)}}{0\left( {r_{0}{\operatorname{<<}r}} \right)} \right.}} & \left\lbrack {e\quad x\quad p\quad r\quad e\quad s\quad s\quad i\quad o\quad n\quad 4} \right\rbrack\end{matrix}$

[0090] It is necessary to input a parameter of a distance r₀ ([μV) . Thestep function type gravitation is expressed by a profile of agravitation as shown in FIG. 7. When the distance between the signaldata and base line becomes shorter than the distance r0, the gravitationworks. Since the presence or absence of the gravitation is decided onlyby judging the distance (μV), there is an advantage such that acalculating process can be omitted. An optional expression can beinputted to the function type and a function which becomes smaller asthe distance becomes longer such as expression 5 shown below or the likecan be used. $\begin{matrix}{{f(r)} = \frac{1}{r}} & \left\lbrack {{expression}\quad 5} \right\rbrack\end{matrix}$

[0091] The flexibility of the base line is set by using the CRT outputdevice 7 from the keyboard input device 6 as shown in FIG. 5A. Hardnesscan be adjusted by a cursor key while watching a flexibility bar graph(FIG. 18) or the hardness can be also picked up on the CRT. The settingcan be changed by the cursor key to select a proper base line even afterthe signal is taken in. Since a medium hard base line is set here, abase line which is like a straight line is obtained.

[0092] From a point of view of strength of materials, the flexibility ofthe base line corresponds to a spring constant or a Young's modulus.Actually, the relative elasticity intensity from 0 to 100 is input. When0 is input, the spring loses the elasticity and becomes like a stringand the base line becomes quite the same as the waveform of the signaldata. When 100 or infinity is input, the base line becomes like a stickof a rigid body having a high rigidity or a straight line which contactsthe signal line with at least two points.

[0093] In FIG. 5B, baseline elasticity is input by a numerical valuefrom a SOFT key. Since a rather soft base line is set, the base line ismore curved. The chromatogram and a calculation result is sent to theprinter output device 7 to be printed using a COPY key.

[0094] In addition to use of the spring constant as a parameter offlexibility, a correction which minimizes a distortion energy of thebase line like an adjustable ruler, a correction like a spline (barflexibility ruler) which minimizes a whole curve, and the like can bealso adapted.

[0095] As a derivative method of the step function type gravitation, abase line envelope method can be considered. An envelope (envelope band)of the distance r₀ is provided above and below the flexible base line.When the signal data exists in the envelope, the base line contacts thedata line, or as shown in FIG. 12, when there is an envelope below thesignal line, the base line is contacted from the lower part. Suchoperations are sequentially repeated, thereby determining the shape ofthe base line. In the method, it is also necessary to input theparameters regarding the distance r₀ (μV) in a manner similar to thestep function type (FIG. 19). This can be regarded as a special casewhere f0 is equal to infinity in the step function type of FIG. 7. Or,this is almost the same as a method where an interval in which thechange amount of a signal is small is regarded as a base portion and ashape which is decided when the flexible base line is contacted from thelower part to the base portion is set to the base line. Further, whenthe elasticity is set to 0, the base line becomes like a string, aportion which is not contacted to the data line becomes a straight lineas if the conventional non-correction method is used.

[0096] As another base line forming means, the base line envelope meansshown in FIG. 29 can be also considered.

[0097] As shown in FIG. 29A, a straight line is contacted to thechromatogram from the lower part with two points (P) and (Q). Anenvelope line of dotted line is shown on an enlarged diagram of the (P)point in FIG. 29B, points r₁, r₂, and 11 on a time base corresponding topoints R1, R2, and L1 on the chromatogram are contacted to the pointsR1, R2, and L1 on the chromatogram in accordance with the order of FIGS.29(C) and 29(D) and the contacting operation is stopped when a point asshown by a point r3 which is deviated from the envelope line appears.The above operation is similarly applied to the (Q) point and the baseline between the (Q) and (P) points is curvedly modified in accordancewith a vector of the base line having a point contacting thechromatogram, thereby enabling a smooth shaped base line to be drawn.

[0098] Advantages of the base line correcting method which is not basedon the base portion or the trough portion will be described by using thechromatogram of glycohemoglobin of FIG. 8 as an example. Hitherto, inorder to correct the base line so that it contacts a trough portionbetween s-Alc and A0, the former six peaks have to be collected in the Nmethod. In actual samples, however, there are not always six peaks. Itcan happen that a trough portion between Ala1 and Ala2 doesn't appear,an F peak disappears, a trough between 1-Alc and s-Alc is not clear, andthe like. Due to this, after taking in the signal data, the number ofpeaks has to be counted again and the N value has to be set again in anoffline post-process. According to the present method, by merely settingthe flexibility to a proper value, a similar base line can be alwaysobtained irrespective of the number of peaks.

[0099] When the flexibility of the base line is desired to be changed inthe middle of the chromatogram, it is set by a time program as shown inFIG. 9A (FIG. 20). When the flexibility of the base line is input as 70at time 0.0 minute and 90 at time 2.5 minutes, the flexibility can bechanged in the interval in a linear gradient manner. A setting can bealso performed by subsequently picking up a starting point of the timeprogram and an intensity of flexibility while watching the chromatogramon the CRT.

[0100] The flexibility can be also input for an interval byexclusive-use input items for the base line correction as shown in FIG.9B. HARD is set for a period of time from 0.0 to 2.5 minutes and MEDIUMHARD is set for a period of time from 2.5 to 7.0 minutes. In this case,although a stepwise switching is performed, it is necessary to locallyperform a gradient switching at a switching point of 2.5 minutes so asnot to have an unnatural curve. As it will be understood from this, onevalue to designate the flexibility for the whole chromatogram ispreferable.

[0101] Similarly, the characteristic distance r₀ can be also set by thetime program (FIG. 21).

[0102] As another embodiment of the invention, a method of detecting abase portion and connecting the base portion by a smooth curve will bedescribed (FIG. 22). An interval in which the signal change amount issmall is searched as a base portion by using parameters such as noise,sensitivity, slope, and the like. FIG. 10 shows a graph made from thebase portions obtained as mentioned above.

[0103] Instead of the conventional method of detecting the base portionon the basis of the signal amount change as mentioned above, a baseportion decided from the relation of gravitation acting between theflexible base line and the signal data line can also be used. A portionwhere the signal data line and the base line contact in the foregoingembodiment is regarded as a base portion (FIG. 5). Portions which arenot contacted are cut, the base portions are left, and a next connectingprocess follows.

[0104] In a manner similar to the foregoing base line envelope method,the flexible base line is contacted to the base portion from the lowerpart, thereby connecting the base portion. A point such that there isthe process exclusively used for searching the base portion in this caseis different from the foregoing base line envelope method. There aredifficulties such that when the rigidity of the base line is too high,an unnaturally curved base line is obtained. When the elasticity is setto be low, the base portion is connected more linearly, and a smoothnesscannot be obtained.

[0105] A spline interpolating method is effective to a connection of thebase portion. In a general spline method, data points are smoothlyconnected by using a cubic polynomial. Since this case relates to theconnection of the base portion comprising a plurality of points, theprocess is slightly different. The base portion is regressed by alinear, quadratic, or cubic expression. The quadratic expression ispreferable. When the regression isn't successfully performed, points onthe connection side of the base portion are used to regress to thequadratic expression. A cubic polynomial for interpolation is determinedso that 0th and first derivatives are equal at an end point on theconnection side of the base portion.

[0106] As shown below, an interpolation expression has four unknownletters, a, b, c, and d. When a regression expression y₁(x) (expression7) of the base portion on the left side and an interpolation cubicpolynomial y(x) (expression 6) make the 0th and 1 ^(st) derivativesequal at an end point L and a similar condition (expression 8) is alsorequested with respect to the right side, four expressions are obtainedand all of the unknown letters can be determined. The connectionconditions in this instance for the left-side and right-side regressionexpressions are shown hereinafter (expression 9).

[0107] interpolation cubic polynomial

y(x)=a+bx+cx ² +dx ³  [expression 6]

[0108] left-side regression expression

y ₁(x)=a ₁ +b ₁ x+c ₁ x ²  [expression 7]

[0109] right-side regression expression

y _(r)(x)=a _(r) +b _(r) x+c _(r) x ²  [expression 8]

[0110] conditions of connection $\begin{matrix}\left\{ {\begin{matrix}{{y_{1}(L)} = {y(L)}} \\{{y_{1^{\prime}}(L)} = {y^{\prime}(L)}}\end{matrix}\left\{ \begin{matrix}{{y(R)} = {y_{r}(R)}} \\{{y^{\prime}(R)} = {y_{r^{\prime}}(R)}}\end{matrix} \right.} \right. & \left\lbrack {{expression}\quad 9} \right\rbrack\end{matrix}$

[0111] The connection of the base portion can be consequently performedby the spline interpolation method.

[0112] As another embodiment, a case of the shoulder peak will bedescribed. The spline interpolation method is also used in principle inthe case. As shown in FIG. 11, the right and left regression expressionof the shoulder peak are smoothly connected by the interpolationexpression, thereby enabling a parent peak and the shoulder peak to beseparated. In this case, a starting point of the shoulder peak is atrough portion and an ending point is, for the convenience, a point ofcontact when a tangent line is drawn from the trough portion to a footportion of the parent peak.

[0113] As a last embodiment, a method of manually correcting the baseline will be described. A point where a base line is likely to exist ispicked up while watching the chromatogram on the CRT (FIG. 26). Althougha method of spline interpolating the picked point can also beconsidered, the method depends on the picked point too much. A method ofusing the flexible base line is also effective (FIG. 27). In this case,the gravitation is allowed to act downward from the data line to thebase line and the gravitation is also allowed to act in the verticaldirection between the picked point and the base line. Since it ispreferable that the base line and the picked point don't largelyseparate, the gravitation of a type which acts stronger as the intervalbetween them becomes longer is selected. For example, a gravitationwhich is proportional to an absolute value of r² or r is suitable. Inthis case, an input of a gravitation constant is necessary. The twokinds of gravitations and flexibility are considered and the balanceequation is solved, thereby determining the optimum flexibility.Consequently, the base line which is imaged by the operator can beobtained. According to such a method, the correction can be similarlyperformed even when a curve like an outline is input.

[0114] An example such that three kinds of base lines when respectiveflexibility i's used are overlaid and displayed is shown in FIGS. 13 and25 (FIGS. 23 and 24). According to the manual pick up method, the properbase line can be selected from the various base lines displayed on theCRT as shown in FIG. 13. Further, by preliminarily picking up a presumedcross point of the base line, the optimum flexibility can be calculated(FIG. 28).

[0115] When the base line is determined as mentioned above, aquantitative calculating process follows. A height or area is used as apeak size. When the calculation is executed on the basis of the peakheight, a value obtained by subtracting a base line Y_(i) from a signalvalue Y_(i) at a point where the peak is largest is set to the peakheight (FIG. 3).

[0116] When the calculation is executed on the basis of the peak area,an area calculation is performed according to the trapezoidal rule orSimpson's rule after obtaining Y_(i)-y_(i) with respect to all of pointsin the peak area.

[0117] It is often necessary to confirm reliability of an obtainedquantitative value. As shown in FIG. 14, coefficients of variation or arelative standard deviation of the quantitative value in each of theflexibilities are output in a format of a table, so that thereproducibility of the quantitative value can be recognized. It will beunderstood from the table that good reproducibility can be obtained whenthe medium flexibility is selected in the case.

[0118] In addition to the table in which the reproducibility is arrangedfor every flexibility, a table in which various quantitative methods arecompared is also effective. For example, the quantitative method basedon the peak area and that based on the peak height, or the conventionalbase line correcting method and the method according to the inventioncan be compared.

[0119] When the base line is formed or corrected, since the base line inwhich the two characteristics of the base line such that the base lineis strongly attracted to the area having the small signal valueexpressed by the chromatogram and that adjacent points among continuouspoints which form the base line are loosely bound are considered can beformed, the base line which is more natural and is not influenced bynoise and the like can easily be drawn by anyone and the base line thatis always stable can easily be provided without a special operation bythe operator.

[0120] By introducing the index of the flexibility that is one of thecharacteristics of the baseline, the base line which is not theconventional temporary base line like a graph of polygonal line but of amore natural and smooth curve can be obtained.

[0121] Although the base line has conventionally been corrected on thebasis of differential characteristic points of a signal such as startingand ending points of a peak, trough between peaks, and the like, thebase line which is not especially influenced by the fluctuation of suchkinds of characteristic points can be obtained in the invention, so thatthe method is not much affected by local changes and noises.

[0122] Thus, the peak size can be accurately determined and the stablequantitative calculation can be always executed.

What is claimed is:
 1. A base line forming method for a chromatographbased on a chromatogram formed with plurality points of chromatogramdata and a straight base line corresponding to said chromatogram,comprising the steps of providing an envelope region formed below saidchromatogram between said chromatogram and an envelope obtained bymoving said chromatogram a distance r_(o), arranging said straight baseline so as to contact two points of data of said chromatogram on thelower side thereof, and moving said base line so as to contact datapoints of said straight base line arranged in said envelope region todata points of said chromatogram corresponding to said data points ofsaid straight base line.
 2. A base line forming method for achromatograph as defined in claim 1, wherein said distance r_(o) isvariable arbitrarily.